A309117 Number of perfect matchings on a triangular lattice of width 4 and length n.

1, 1, 5, 15, 56, 203, 749, 2777, 10293, 38240, 141997, 527593, 1960029, 7282483, 27057400, 100531559, 373522965, 1387822193, 5156442953, 19158736256, 71184183353, 264484479633, 982690786037, 3651182836279, 13565952140920, 50404229548515, 187276671274621

Offset

0,3

Links

Table of n, a(n) for n=0..26.

S. N. Perepechko, Number of perfect matchings on triangular lattices of fixed width, DIMA'2015 slides.

Formula

G.f.: (1-z)*(1+z)*(1-z-5*z^2-z^3+z^4)/((1+z-3*z^2-3*z^3+z^4)*(1-3*z-3*z^2+z^3+z^4)).

Crossrefs

Cf. A011900, A307349.

Sequence in context: A137959 A001552 A165731 * A307349 A343841 A203294

Adjacent sequences: A309114 A309115 A309116 * A309118 A309119 A309120

Keyword

nonn,easy

Author

Sergey Perepechko, Jul 13 2019

Status

approved